ABCD is a square. A is joined to a point P on b c and d is joined to a point Q on AB.if Ap = DQ prove that a b and dq are perpendicular to each other
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Proving the congruency of triangles PAB &DAQ
PA=DQ
angle B=angle A( since they both are 90°)
AB=AD( since both of them are sides of the square)
therefore the triangles are congruent by RHS axiom.
angle DAP+angle PAB=90°
and angle PAB = angle QDA (by CPCT)
therefore angle DAP+ angle QDA=90°
therefore angle DMA=90° ( considering triangle DMA and applying the angle sum property of triangles).
I'm sorry since my camera is not working I've sketched your diagram...it might seem untidy but hope you understand
PA=DQ
angle B=angle A( since they both are 90°)
AB=AD( since both of them are sides of the square)
therefore the triangles are congruent by RHS axiom.
angle DAP+angle PAB=90°
and angle PAB = angle QDA (by CPCT)
therefore angle DAP+ angle QDA=90°
therefore angle DMA=90° ( considering triangle DMA and applying the angle sum property of triangles).
I'm sorry since my camera is not working I've sketched your diagram...it might seem untidy but hope you understand
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i hope it helps
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